TY - GEN

T1 - Incremental Robbins-Monro gradient algorithm for regression in sensor networks

AU - Sundhar Ram, S.

AU - Veeravalli, Venugopal Varadachari

AU - Nedich, Angelia

PY - 2007/12/1

Y1 - 2007/12/1

N2 - We consider a network of sensors deployed to sense a spatial field for the purposes of parameter estimation. Each sensor makes a sequence of measurements that is corrupted by noise. The estimation problem is to determine the value of a parameter that minimizes a cost that is a function of the measurements and the unknown parameter. The cost function is such that it can be written as the sum of functions (one corresponding to each sensor), each of which is associated with one sensor's measurements. Such a cost function is of interest in regression. We are interested in solving the resulting optimization problem in a distributed and recursive manner. Towards this end, we combine the incremental gradient approach with the Robbins-Monro approximation algorithm to develop the Incremental Robbins-Monro Gradient (IRMG) algorithm. We investigate the convergence of the algorithm under a convexity assumption on the cost function and a stochastic model for the sensor measurements. In particular, we show that if the observations at each are independent and identically distributed, then the IRMG algorithm converges to the optimum solution almost surely as the number of observations goes to infinity. We emphasize that the IRMG algorithm itself requires no information about the stochastic model.

AB - We consider a network of sensors deployed to sense a spatial field for the purposes of parameter estimation. Each sensor makes a sequence of measurements that is corrupted by noise. The estimation problem is to determine the value of a parameter that minimizes a cost that is a function of the measurements and the unknown parameter. The cost function is such that it can be written as the sum of functions (one corresponding to each sensor), each of which is associated with one sensor's measurements. Such a cost function is of interest in regression. We are interested in solving the resulting optimization problem in a distributed and recursive manner. Towards this end, we combine the incremental gradient approach with the Robbins-Monro approximation algorithm to develop the Incremental Robbins-Monro Gradient (IRMG) algorithm. We investigate the convergence of the algorithm under a convexity assumption on the cost function and a stochastic model for the sensor measurements. In particular, we show that if the observations at each are independent and identically distributed, then the IRMG algorithm converges to the optimum solution almost surely as the number of observations goes to infinity. We emphasize that the IRMG algorithm itself requires no information about the stochastic model.

UR - http://www.scopus.com/inward/record.url?scp=50249131938&partnerID=8YFLogxK

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U2 - 10.1109/CAMSAP.2007.4498027

DO - 10.1109/CAMSAP.2007.4498027

M3 - Conference contribution

AN - SCOPUS:50249131938

SN - 9781424417148

T3 - 2007 2nd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMPSAP

SP - 309

EP - 312

BT - 2007 2nd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMPSAP

T2 - 2007 2nd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMPSAP

Y2 - 12 December 2007 through 14 December 2007

ER -